OK, everyone, thanks for all the replies.
I don't have any other Ataris to test the chips with, I broke (and fixed) the bypass capacitor connected to U33 (which I now think is the bit 7s of the upper 64K). I don't think anything else is broken, although my problems initially came via the cartridge slot, so who knows. I assume the new RAM chips are fine, as I've just bought them (although that's not 100% guarantee).
Regarding the old thread, I had looked at that but everything had been about testing the number of banks above 64K, not the integrity of the bottom 64K/128K. But... I had another look and there was one thing there that did what I wanted: SUPERSAL.COM (for the lower 64K, at least).
It told me that bit 6 was suspect in the range $6000-$7FFF, so I swapped U15 with U32 and it reported the lower 64K as all working. I swapped the upper set of chips with the lower set of chips and tried again - all OK... This was a bit surprising, because it naturally contained the chip that was causing the problem before... however, it seems to be holding for now.
Fingers crossed that it stays that way!
Thanks for all the help.